# If two people pull on either side of the rope with a force of 65N, why is the tension in the rope 65N?

Apply Newton's third law. See below.

The rope experiences the same pulling force on both sides, and therefore it is in a state of static equilibrium (i.e. it is at rest consequently has a net force of zero).

A force diagram:

Where

#vecF_1# and#vecF_2# are the pulling forces on the rope and#vecT# is the tension force.#R# will represent the rope later.Here we consider Newton's third law.

Newton's third law states that every force occurs as a member of an action/reaction pair of forces. You may know it as the familiar phrase, "every action has an equal and opposite reaction." Most importantly, two members of an action/reaction pair are equal in magnitude but opposite in direction.

#vecF_(A on B)=-vecF_(B on A)# In this situation, each person pulls on the rope with

#65N# of force, so:

#vecF_(1 on R)=65N# and#vecF_(2 on R)=65N# .This tells us that the pulling force exerted by each person on the rope is

#65N# , and consequently by NIII, the rope exerts an equal but opposite tension force of#65N# on each person.This is an action reaction pair. Therefore:

#vecF_(R on 2)=vecF_(2 on R)=vecF_(1 on R)=vecF_(R on 1)=65N# The tension force in the rope, given by

#vecF_(R on 1)# and#vecF_(R on 2)# , is therefore#65N# .

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The tension in the rope is 65N because the rope is assumed to be massless and inextensible. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When each person exerts a force of 65N on the rope, the rope applies an equal and opposite force of 65N on each person. Therefore, the tension in the rope is also 65N, as there is an equilibrium of forces acting on the rope.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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